Device for predicting values of a fluctuating system at a predetermined future time



April 4, 1961 w. H, NEWELL ErAL 2,978,177

DEVICE FOR PREDICTING VALUES 0F A FLUCTUATING SYSTEM AT A PREDETERMINEDFUTURE TIME Original Filed May 29. 1953 7 I l l l lf s To, w w p 2 1 )Ws p/ m f K T R C 0 2 :L f T d, T V n P2 m... u M u wf v L G/ w. J Y- R ZK U u U E r M M 2 M M s /3 P n e To, o pp f Kl W w .U w 6 o r. AM A ,KIMW lpv w. AS f, MIL M E M J 5 7o, 6 y 3 w 2 N Per z/f ,If w P2 M 3 2 m Z.H 2 W p K1 K m s 1 m p1 w TW P1 m .9 M J w A m W U W N 27. n K +A To,/zl p w 2 l C l. 1 i A( K f Y /l y L w n WN O S NsGZN .4 1 u .m M EffAGAS 02%. if @MMM N w m 5 w 4W E ,lvilm a. la

DEVICE FOR PREDICTING VALUES F A FLUC- TUATING SYSTEM AT A PREDETERMINEDFUTURE TIME riginal application May 29, 1953, Ser. No. 358,324. and thisapplication Dec. 17, 1954, Ser. No.

5 Claims. (Cl. 23S-186) The present application is a division ofapplication Serial No. 358,324, filed May 29, 1953.v

The present invention relates to a method and -apparatus for computingthe characteristics of a fluctuating system continuously` for successivefuture periods, and although it has a wide range of utility, it isparticularly useful in predicting the future pitch angle (deck tilt) andthe future heave (level) at a future time of a floating platform, suchas the flight deck of a carrier. l

In guiding an airplane in its approach towards a oating platform, suchas the deck of a carrier, lfor landing, it is necessary to predict thetime of landing and the pitch angle and heave of the deck at thepredicted time, to assure safe landing. Since the carrier iscontinuously oscillating in pitch and has a continuous oscillatingvertical movement, during the approach of the airplane, it

becomes necessary to compute continuously the charac` teristics of thefluctuating motions of the carrier and to predict therefrom the pitchand heave of the carrier at the future predicted time of landing. Sincethe move'- ment of the deck plane does not follow a uniform mathematicalpattern or equation, it is seen that the matter of determining withaccuracy the pitch and heave at a future time is not a simple problem.

One object of the present invention is to provide a novel device bywhich the characteristics of a fluctuating system may be 'computed andpredicted continuously for successive future periods, even though theform of the system may be continuously varying and the variations in thesystem may not be following continuously any predetermined mathematicalpattern or equation.

Another object is to provide a novel device by which the future pitchangle of a floating platform, such as the flight deck of a carrier, atthe expected future instant of landing can be computed and predicted.

the future heave or flight deck level of a floating platform, such asthat of a carrier, at the expected future instant of landing can becomputed and predicted.

In carrying out the invention, the value of a certain quantity at afuture time in a fiuctuating system is computed continuously, bycomputing at each instant from the present value of said quantity andfrom the future time, the predicted future value of the quantity at saidIfuture time, based on the assumptionrthat the characteristics of thesystem at any instant continues from that instant to said future time inaccordance with a definite mathematical pattern, and as the subsequentvalues of said quantity deviate from any assumed characteristic of thefluctuating system and follow a new characteristic of a differentmathematical pattern, recomputing the predicted value of the quantity atthe future time based on the assumption of the new characteristic of thefiuctuating system. v

In its more specific aspects, the invention is employed for continuouslypredicting the pitch angle and heave Ptented'Apr.' 4, 1961 of thefloating platform at a future time by computing at each instant from thepresent pitch angle and heave and from the future time the predictedpitch/angle and heave based on the assumption that the fluctuations inpitch angle and heave follow sine waves respectively of definiteconfigurations from that instantto the future time, and as thesubsequent values of pitch angle and heave deviate from respective sinewaves Vof assumed configurations and follow the sine waves of differentconfigurations, recomputing the predicted pitch angle and heave on thevbasis of sine waves of said different configurations.

Various other objects, features and advantages of the present inventionare apparent from the following particular description and'fromaninspection of the accom-- panying drawings, in which Fig. l is adiagrammatic view of an integrator typeA follow-up employed inconnection with a form of mechanism for determining the predicted pitchangle of the deck at any future time in accordance with a simplified:equation; and

Fig. 2 is a diagrammatic view of a form of mechanism employingintegrator type follow-ups o-f Fig. l for deter mining the predictedpitch angle of the deck at any futurei time in accordance with asimplified equation, the solid. lines indicating mechanical motion andthe dotted lines electrical signals.

To predict the position of a ships deck at` the futurev instant oflanding `of an approaching plane, it is required that the time aheadwhen the airplane is expected to land be predicted and then that theposition of the deck at this time be predicted. This sequencefofpredictions is based on the assumption that the pilot has sole controlof the plane speed and that the position of the deck at touchdown (theposition on the deck Where the plane can begin to land) is notpreselected.

The time required by a plane to fly from its present position to itsposition at touchdown on the deck indicated herein by the symbol Tp canbe calculated in the f continuously the present pitch angle of the deckindicated by the symbol P0 and the present deck height indicated by thesymbol HU.

To supply continuously information on the magnitude of the present shippitch angle, service of a stable ele,

ment is required. This stable element could be of any well knownconstruction.V For example, it could be one of the stable elementscommonly employed in connec- A further object is to provide a noveldevice by which 'Y tion with firing control systems on warships, exceptthat it would be provided with means for transmitting the pitch` P0 tothe system, for example intheform of Ya shaft rotation. There is alsothe possibility that the stable lizer unit required in connection withtheradar antenna `drive could also be used to supply the information P0.There is also in existence a pitch and roll recorder. This unit mightalso be used, if the accuracy and smoothness of operationwerefsatisfactory for the purpose in mind,

Continuous measurement and supply ofthe H0 that is the vertical motionof the ship may be effected by an accelerometer of the type shown anddescribed in the aforesaid copending application.

Having determined a value for lthe prediction time Tp, the second phaseof the prediction problem is entered into, namely the deck tilt Pp atthe future time Tp. Consider first a ship at rest in still water. `Ifnow a moment should be applied about an athwartship axis through thecenter of gravity, Vsome pitchangle, say P would result. Upon removal ofthis applied moment, the ship would oscillate` in pitch about theathwartship "2,978,177 I- Y e axis with decreasing amplitude, theequation of motion being approximately IF+CP+KP= (1s) where fl is theeffective longitudinal moment of inertia of the ship about theathwartship pitch axis, 'C is the damping moment coeflicient due to skinfriction and the like, K vis the hydraulic restoring moment coefficient,l is the second derivative of the pitch angle, with respect to time andP is the first derivative of the pitch angle with respect to time. Nowthe period of this oscillation is the pitching period of the ship and isequal to where wnp=natural angular frequency of pitch. However, when theship is in a Seaway, the equation of motion 18 becomes where F (t)represents the pitch component of the moment applied to the ship by waveaction. Now from general observation, it can be .said that F(t),although highly variable, will nevertheless at a given hour exhibit afrequency spectrum in which certain narrow bands of .frequencies arepredominant. From an analyzed recording of pitch angle of various typeships headed into the wind under different sea conditions over extendedperiods of time, it would be possible to obtain the frequency spectrumof the ships pitching motion under the conditions existing at the timeof the run. -From this data, it would be noted that the frequencies ofgreatest amplitude would correspond to the natural pitch period of theship, the periods at which the ship is encountering the particular wavesystems running at the time, the period of ship roll and the period ofheave. The last two periods mentioned would probably be of small importand are included only because of the fact that both rolling and heavingcause an induced pitch. Usually, but not always, there will be a singlesystem of waves running. Furthermore, this system of waves will moreoften than not be running in nearly the same direction as the wind.Hence, the normal expectation during carrier landing operations is thatthe ship would be headed in a direction about opposite to that in whichthe waves are traveling. Considering that the usual period of oceanwaves is in the range of 5 to l0 seconds, a ship speed of 25 knots wouldreduce these periods to the range of 1.8 to 5.5 seconds. It almost seemsfrom these considerations that under such conditions, the only period tobe seriously considered in pitch motion would be the natural pitchperiod. That is, a forcing moment function of 2 second period would haveto be of tremendous magnitude to appreciably affect the ship motion inpitch. However, a forcing function of 5 second period might well have anappreciable effect, and of course a longer period forcing function wouldhave still greater influence. Functions having such longer periods wouldarise if the normal conditions outlined above did not hold-as forexample, when the wind is opposite in direction to the sea and the shipis traveling with a following sea. From the above discussion, it isevident that an exact solution for the Vequation of motion of the shipis not possible. However, the equation of motion may be represented withsuicient accuracy by the approximation 1i3+KP=Fo =a sin (WH-a) whereF(t) is a sine function of unknown amplitude a, angular frequency w andphase angle qt. The solution of this differential equation is then ofthe form P=r11` sin (wifi-@Haz sin (wm-#2) (20) w1 and W2 being theunknown angular velocities and 1 and p2 the phase angles of theV simpleharmonic motions of which the pitch angle is assumed to be composed.This form, involving the six unknown parameters a1, a2, w1, wz, p1 andpz therefore represents the time variations of pitch angle. Hence, ifthese six unknowns and variable parameters can be continuouslydetermined and furthermore if a continuous value of prediction time Tpis available, then the predicted pitch angle is The problem is nowtherefore reduced to the continuous determination of the six unknown andvariable parameters noted above.

In the form of mechanism which can be employed in accordance with thepresent invention to determine the predicted pitch angle Pp, it isassumed in Equation 2O that a1=a and 112:0, so that P=a sin (wt-l-qb)(22) Considered here as known quantities are the present value of pitchangle P as well as the rates of change P, P, etc. Furthermore, if meansare provided for recording P, the values of P and its rates at any pastinstant of time will be known. From this known data, the quantities a, wand p which are for the present considered to be constants, must bedetermined. Now this evaluation is carried out in accordance with thepresent invention in the manner described herein.

Suppose for instance that Equation 22 is rewritten in the form P: geawwwi.; awww (23) where a, w and qb are unknown constants, and let P beconnected to an integrator type follow-up as shown in Figure l. Thisfollow-up comprises a substracting differential 111 and an integrator112 with a time constant K1 and an output P1 consituting one of theinputs of the differential, the other input being the quantity P. Thenin operational notation,

Here, since the sine wave is assumed to have a. w and qa constant, thetransient term -t CleKi K1 may be dropped for steady state conditionswith the result that Similarly, if P is connected to a secondintegration type follow-up similar to that shown in Figure 1, there isobtained the quantity P2: 2(1+ Kawa It is now possible to eliminate thetwo quantities iaeitwwa) from the three Equations 23, 24 and 25. vTheresult of this ehmination written in determinant form. is

The expansion of this determinant gives the value w3 Having determined wfrom Equation 26 as the positive square root of the expression on theright hand side and knowing the prediction time Tp, the predicted pitchangle Px, can be determined PD: aetwrwitwww j Zl-twrme-itwt-wn V(27) Asbefore, the quantities may be eliminated from the three Equationsv 23,24 and 27. The result of this operation gives the determinant relation rthe value Pp is shown diagrammatically in Figure 2, the

solid lines indicating mechanical movement, the dotted lines indicatingelectrical signals. In this mechanism, the quantity P which isequivalent to P previously discussed, i.e. the present pitch angle,derived from the stable element is introducedinto the integrator typefollow-up unit 110 is previously decribed and shown in Figure l, to ob-A tain the output P1 which by proper gear ratio becomes K12K2P1 and thesame quantity P is introduced Yintop'a second integrator type follow-upunit 115 with proper gear ratio to obtain an output quantity K1K22P2.The nwo output quantities K12K2P1 and K1K22P2 are subtractedr in adifferential gear 116 to give an output quantity K1K2(K1P1K2P2) which ismultiplied. in a unit.117V by W2. to. give the quantityK1K2(I(1P1K2P2)W2. latter quantity and the quantity K2(P-P1)-K1(P-P2)derived asthe output of a differential 118 having input K1P1 equal toP-P1 and input K2P2 equal to P-P-z, multiplied by proper gear ratios K2and K1 respectively, are fed into a differential 120 to obtain thedifference between K1K2(K1P1K2P2)w2- and f This diiherence operatesfollow-up contacts 121 controlling a servo motor 122, and when thisdifference is zero,

the contacts are opened and the servo motor shaft will quantity Tladerived from the prediction time computer are multiplied together in aunit 124 and the resulting product wTp isintroduced into a resolver 125to obtain component quantities sin wTp and cos wTp. The quantitysin WTS,is` fed into a multiplier 126 in conjunction with theY quantity1+K12iv2, obtained by proper Vgear ratio and offset of the output w2obtained from the multiplier 123, to obtain the product (l-l-K12w2) VsinwTp which is v multiplied in the unit 127 by the quantity P1 obtained byproper gear ratio from the output of the integrator type follow-up unit110 to obtain the quantity A u The other. component quantity cos wT fromthe resolver 125 is fed into a multiplier 130 and multi- This latterquantity and the quantity K1wP1J obtained from the output of amultiplier 134 into which the magnitudes Pp and K1w are f ed areintroduced into a differential 135 to obtain the diierence between K1wPpand This dilference operates follow-up contacts 136 controlling servomotor 137, and when this difference is zero, the contacts are opened andthe servo motor shaft will have rotated through an angle correspondingto the value of Pp in accordance with Equation 28.

Equations 26 and 28 may be mechanized by the mechanism of Figs. 1 and 2,to determine the value of Hp (predicted deck height at predicted timeT1, of landing) exactly as was the value Pp (predicted pitch angle ofthe carrier at the predicted time T In that case, Equation 26 becomesand Equation 28 becomes H representing the present value of the deckheight equivalent to H0 and H1 and H2 being derived from integrator typefollow-ups, similar to the .follow-ups 110 and 115 of Fig. 2.

The mechanism of Figs. l and 2 may be set up as part of a system forguiding an airplane in its approach towards the flight deck of acarrier, as shown and described in the aforesaid copending application.However, as far as certain aspects of the invention are concerned, themethod and mechanism of the present invention may -be employed forcontinuouslyv predicting the future value of a quantity in a fluctuatingsystem. As willbe noted, as the present values of the quantity arecontinuously fed into the mechanism, the future value of the quantity ata predetermined or predicted future time is computed on the assumptionthat the quantity undergoes a fluctuation of constant mathematicalcharacteristic (sine wave in the more specific aspects of the invention)and as the quantity of presentvalue continuously received deviates invalue from this assumed characteristic, the value of the quantity atsaid future time is continuously recomputed until said future timearrives.

In the following claims, the symbols Tp, P and Pp have the generalmeanings indicated with application generally to a fluctuating system,unless specifically defined.

What is claimed is:

1. A device for predicting the value of a uctuating system at a futuretime Tp Vknowing the presentvalue of 7 the system P, comprising meansfor mechanizing and solving the equations K12K2P1 and K1P1 and the other'for obtaining the quantities K1K22P2 and KZPZ, each of said follow-updevices comprising an integrator, a differential having a P input, afeed-back input from the output of said integrator and an output forsetting the quantity to be integrated into said integrator, in saidequations and in said quantities, K1 and K2, representing the timeconstants of said integrators respectively, P1 and P2 theoutputs of saidintegrators respectively, P1 and'Pz the rst derivations of P1 and P2respectively, and w the angular velocity of the simple harmonic motionof which said system is assumed to be composed, means for comparingK12K2P1 and K1K22P2 to obtain K1K2(K1P1K2P2), means for multiplying the.latter quantity by w2 to obtain K1K2(K1P1-K2P2)w2,

to obtain a quantity which is theoretically zero, but which deviatestherefrom by an error amount, a servo mechanism having as an input theerror quantity to eifect a null seeking operation and to obtain therebyw, means for squaring W t Obtain lVZ I 1K2(K1P1-K2P2) iS means formultiplying Tp by w to obtain wTp, a resolver having as input wTp forobtaining cos wTp and sin wTp, means for multiplying w by K1 to obtainKlw, means for multiplying the latter quantity by cos wTp to obtain Klwcos wTp, means for adding the latter quantity and sin wTp to obtain K1cos wTp-lsin wTp, means for multiplying the latter quantity by P toobtain (Klw cos wTp+ sin wTp) P, means for processing W2 to obtain1+K12w2, means for multiplying the latter quantity by sin wTp to obtain(1+K12w2) sin wTp, means for multiplying the latter quantity by P1 toobtain (1+K12w2)P1 sin wTp, means for adding the latter quantity ot thequantity (Klw cos wTp-lsin wTp)P equal theoretically to zero anddeviating therefrom by an error quantity, and a servo mechanism havingas an input the latter error quantity to effect a null seeking operationand to obtain thereby Pp, the latter quantity being employed as a-factor for Klw to obtain KlwPp.

2. A device for predicting continuously the value Pp of a sinusoidalsystem at a future time Tp having available a continuing signalcorresponding in magnitude to the present values P of the system and forobtaining said value Pp as a physical quantity in the form of a signal,comprising means responsive to a continuous signal corresponding inmagnitude to the continuing values P for mechanizing and solvingcontinuously the equations.

and

for the predicted value Pp and for obtaining a continuing signalcorresponding in magnitude to the solved Pp, and including twointegrator follow-up devices, each including an integrator forintegrating in relation to time, a differential having a P input, afeed-back input from the output of said integrator and an output forsetting the quantity to be integrated into said integrator, one of saidintegrator follow-up devices computing the value K1K22P2 and the otherfollow-up device computing the value K12K2P1 and a differential forcomparing the outputs of said integrator follow-up devices to obtain thevalue K1K2(K1P1-K2P2), in said equations, K1 and K2 representing thetime constants of said integrators respectively, P1 and P2 the outputsof said integrators respectively, and w the angular velocity of thesimple harmonic motion of which said system is assumed to be composed,and means for continuing the operation of said mechanizing and solvingmeans until the future time Tp has been reached, whereby `a continuoussignal is obtained approaching in magnitude the true value of Pp as thefuture time Tp is approached.

3. A device as described in claim 2 for predicting the pitch angle of vaoating deck at a future time Tp knowing the present pitch angle of thedeck, wherein P represents the present pitch angle of the deck and Ppthe predicted pitch angle of the deck at the future time Tp.

4. A device as described in claim 2 for predicting the height of aoating deck at the future time Tp, knowing the present height of thedeck, wherein P represents the present height of the deck and Pp thepredicted height of the deck at the future time Tp.

5. A device for predicting the value of a fluctuating system asdescribed in claim 2, wherein said device comprises means responsive toinput P and including said integrator follow-up devices, for obtainingthe quantities means for comparing the last two mentioned quantities forobtaining a quantity which is theoretically zero but which deviatestherefrom by an error amount, means having as input said error quantityfor solving the equation.

as an input the last-mentioned error quantity for solving the equationKlwPp-(Klw cos wTp-l-sin wTp)P +(1+K12w2)P1 sin wTp=0 for the quantityPp.

References Cited in the tile of this patent UNITED STATES PATENTS2,404,011 White July 16, 1946 2,407,665 `I-lolschuh et al. Sept. 17,1946 2,442,792 White et al. June 8, 41948 OTHER REFERENCES ElectronicInstruments (Greenwood), pages 131 to Product Engineering (Reid et al.),August 1949, pages 131-135, September 1949, pages 119-123, October,1949. pages 126-130; November, 1949, pages 121-124.

Electron-tube Circuits (Seely), pages 164 to 165, 1950.

